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Math 920 (922) Class Syllabus Fall Semester 2011 Functional Analysis

Summary: Math 920 (922) Class Syllabus Fall Semester 2011
Functional Analysis
Lecture: Monday, Wednesday, Friday, 3:00 3:50 in room C211 Wells Hall
Instructor: Prof. Casim Abbas
A202 Wells Hall
phone: 353 8499
Office hours: Monday, Wednesday, Friday, 4:10-5:00 or by appointment
Textbook: Haim Brezis; Functional Analysis, Sobolev Spaces and Partial, Differential Equations;
Springer (an electronic copy is available from the MSU library webpage). I will use my
lecture notes from the Spring semester of 2003 which are available on my webpage.
Topics covered: Normed linear spaces (Examples of Banach spaces, Ascoli-Arzela theorem, Frechet-
Kolmogorov theorem, uniform convexity), Linear operators (Banach-Steinhaus theorem,
open mapping principle, topological complements), Hilbert spaces (Riesz representation
theorem, Lax Milgram lemma, Radon Nikodym theorem), Hahn Banach theorem, Dual
spaces, Reflexivity, Weak and weak * convergence, Milman's theorem, Spectrum of
compact operators.
Grades: I expect that you attend classes regularly and that you complete the occasional
homework assignments.
Important dates:


Source: Abbas, Casim - Department of Mathematics, Michigan State University


Collections: Mathematics